Question 1175652: Michael will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $42 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $51 and costs an additional $0.12 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If he drives x miles, then...
The cost for the first plan is 42+0.14x
The cost for the second plan is 51+0.12x
You want to know when the costs for the two plans will be the same, and what that cost will be.
In practice, by far the easiest way to solve the problem is to graph the two functions on a graphing calculator and find the x and y values (number of days and cost, respectively) where the two graphs intersect.
With formal algebra, which is probably what you as the student are probably supposed to be doing....
You want to solve the equation that says the costs for the two plans are the same:
42+0.14x = 51+0.12x
0.02x = 9
x = 9/0.02 = 450
ANSWER 1: The two plans cost the same for driving 450 miles.
Plug that number of miles into either (or both) of the formulas for the costs of the two plans to find the cost. Obviously the two results should be the same; if not, then there is something wrong with your calculations.
I leave it to you to finish the second part of the problem.
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